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Partial λ-Geometries and Generalized Hadamard Matrices Over Groups

Published online by Cambridge University Press:  20 November 2018

David A. Drake
David A. Drake*
Affiliation:
University of Florida, Gainesville, Florida
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Section 1 of this paper contains all the work which deals exclusively with generalizations of Hadamard matrices. The non-existence theorem proven here (Theorem 1.10) generalizes a theorem of Hall and Paige [15] on the non-existence of complete mappings in certain groups.

In Sections 2 and 3, we consider the duals of (Hanani) transversal designs; these dual structures, which we call (s, r, µ)-nets, are a natural generalization of the much studied (Bruck) nets which in turn are equivalent to sets of mutually orthogonal Latin squares. An (s, r, µ)-net is a set of s2µ points together with r parallel classes of blocks. Each class consists of s blocks of equal cardinality. Two non-parallel blocks meet in precisely µ points. It has been proven that r is always less than or equal to (s2µ – l) / (s – 1).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 3 , 01 June 1979 , pp. 617 - 627
Copyright
Copyright © Canadian Mathematical Society 1979

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